Electrical characterization of photovoltaic cells to predict cell performance

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ELECTRICAL CHARACTERIZATION OF

PHOTOVOLTAIC CELLS TO PREDICT CELL

PERFORMANCE

By: Alexander Eick

GRADUATION REPORT

Submitted to

Hanze University of Applied Sciences Groningen

in partial fulfilment of the requirements for the degree of

Fulltime Honours Bachelor Advanced Sensor Applications

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ABSTRACT

ELECTRICAL CHARACTERIZATION OF PHOTOVOLTAIC CELLS TO PREDICT CELL PERFORMANCE

by Alexander Eick

The predicted depletion of fossil fuel reservoirs, together with rising energy demands and an increasing environmental awareness make the production of energy from environmenta l ly friendly and renewable sources necessary. One of those sources is solar power, from which energy can be harvested with photovoltaic panels.

The research presented here is aimed at modelling the output of photovoltaic modules using exclusively electrical parameters at standard test conditions (STC), usually provided by the manufacturer. This will enable power producers to predict their output accurately and effectively. Furthermore, it can help the industry to identify defects and shortcomings in newly developed solar cells and modules faster, thus reducing the development risks.

Presented results verify the proper operation of the proposed model. The validation process shows good results with Nash-Sutcliffe model efficiency coefficients above 0.95, for high and medium irradiance levels. At low irradiance levels the proposed model results in higher errors. However, further tests, with various other photovoltaic modules are needed to validate the proposed model completely.

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DECLARATION

I hereby certify that this report constitutes my own product, that where the language of others is set forth, quotation marks so indicate, and that appropriate credit is given where I have used the language, ideas, expressions or writings of another.

I declare that the report describes original work that has not previously been presented for the award of any other degree of any institution.

Signed, 18/01/2015

……….. Alexander Eick

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ACKNOWLEDGEMENTS

I would like to express my great appreciation to Prof. Dr. Davies William de Lima Monteiro for giving me the opportunity to conduct research in the field of renewable energy, specifica l ly photovoltaics. He has provided me with excellent guidance and invaluable feedback. Furthermore, I am in debt to all the members of the Optronics and Microtechno lo gy Laboratory, especially Poliana Henriques Bueno, André Luiz Costa de Carvalho and Diogo Ferraz Costa, of the photovoltaics group, for their continuous help and patience. They always had an open ear for my questions and assisted me with their vast knowledge.

My thanks are as well extended to Dr. Ronald A.J. van Elburg for his feedback on the deliverables and his guidance throughout the whole project.

I would like to show my appreciation to the staff of the Institute of Engineering, location Assen, for their support during my study and for preparing me for my graduation.

I wish to thank the Federal University of Minas Gerais (UFMG) and the Hanze University of Applied Sciences for offering me the possibility of graduating abroad.

Credit should also be given to my friends, who reviewed my thesis and provided me with feedback.

Finally, I am deeply thankful for the unconditional love and support of my family and my girlfriend, who encouraged me to pursue my dreams and who made me who I am.

Thank you all for your support and tolerance.

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LIST OF FIGURES

Figure 2-1 Primary energy supply in relation to the world population ... 4

Figure 2-2 Predicted electricity generation between 2010 and 2050 by source ... 5

Figure 2-3 Primary energy production of Brazil in 2013 ... 6

Figure 2-4 Electricity supply of Brazil in 2013 ... 6

Figure 2-5 Annual average of daily inclined solar irradiation in Brazil (25) ... 7

Figure 2-6 Spectrum of AM1.5G ... 8

Figure 2-7 Bohr model of silicon (31)... 9

Figure 2-8 Schematic drawing of a silicon solar cell (32)... 9

Figure 2-9 Schematic of the operating principle of a silicon solar cell (34) ... 10

Figure 2-10 Typical I-V curve of a photovoltaic cell ... 11

Figure 2-11 Factors influencing photovoltaic cell output ... 13

Figure 2-12 Typical forward bias characteristic of a p-n junction diode ... 14

Figure 2-13 PSPICE A/D interface ... 16

Figure 2-14 PSIPCE components in OrCAD Capture (46) ... 17

Figure 2-15 One-diode solar cell model ... 18

Figure 2-16 Two-diode solar cell model ... 19

Figure 3-1 Flowchart of the general concept... 21

Figure 3-2 Schematic of the proposed solar cell model ... 23

Figure 3-3 Circuit schematic of the proposed model ... 28

Figure 6-1 Simulation results of the four models at 100°C ... 34

Figure 6-2 Simulation results at 250 W/m2_{and 25°C with variable and constant} Rs... 37

Figure 6-3 Simulation results of the proposed model at 30°C ambient temperature and two different Rs configurations ... 39

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Figure 6-5 Dataset 1 fitted I-V curve and simulation results (up) and absolute

error (down) ... 41

Figure 6-6 I-V curves and error plots of the fitted curve and the simulations for Dataset 2 ... 43

Figure B-1 OrCAD circuit of the first model used in chapter 5.1.1... 61

Figure B-2 OrCAD circuit of the second model used in chapter 5.1.1 ... 62

Figure B-3 OrCAD circuit of the third model used in chapter 5.1.1 ... 63

Figure B-4 OrCAD circuit of the fourth model used in chapter 5.1.1 ... 64

Figure E-1 Voc, Isc, Vm and Im for different ambient temperatures ... 81

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LIST OF TABLES

Table 6-1 Comparison of four models using intrinsic diode and resistor

models and analog behavioral models, at 25°C, 50°C and 100°C ... 33

Table 6-2 Key simulation results for different irradiances with constant Rs ... 35

Table 6-3 Key simulation results for different irradiances with variable Rs ... 36

Table 6-4 Key simulation results for different ambient temperatures and constant Rs... 37

Table 6-5 Key simulation results for different ambient temperatures and variable Rs ... 38

Table 6-6 Errors and model efficiency values for the proposed and Castaner´s model... 42

Table 6-7 Measurements and simulation results of key parameters together with their respective errors... 42

Table 6-8 Output errors of the model for maximum error of the input parameters ... 44

Table E-1 Raw data of the comparison between ABM and intrinsic modelling at 25ºC and 50ºC ... 69

Table E-2 Raw data of the comparison between ABM and intrinsic modelling at 100ºC ... 70

Table E-3 Raw data of simulation with changes in irradiance, where Rs in constant and variable... 72

Table E-4 Raw data of simulation with changes in ambient temperature, where Rs is constant and variable ... 76

Table E-5 Key simulation results different ambient temperatures and constant Rs ... 80

Table F-1 Measurements performed with Solmetric PVA-600 PV Analyzer ... 82

Table F-2 Raw data of validation simulations for dataset 1 and 2 ... 84

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ABBREVIATIONS

AM1.5G Air Mass of 1.5

Air mass number that represents the solar spectrum at mid-latitudes, where the sun is at an angle to the earth´s surface, thus increasing the effective thickness of the atmosphere.

BRIC Acronym for Brazil, Russia, India, China

Group of countries which are at similar stages of their economic

development. The acronym acknowledges the apparent shift in economic power away from the developed countries towards the developing nations.

CANCER Computer Analysis of Nonlinear Circuits, Excluding Radiation

General circuit analysis program that is especially suited to integrated-circuit simulation.

CCS Carbon capture and storage

A method of capturing carbon dioxide and depositing it at sites where it cannot enter the atmosphere.

CEMIG Companhia Energética de Minas Gerais

The state electrical energy-distribution company of Minas Gerais

CIGS Copper indium gallium selenide solar cells

A widely spread thin film solar cell made from the mentioned materials.

GCF Green Climate Fund

A foundation to provide easy access to funding for projects that will contribute to the achievement of the ultimate objective of the United Nations Framework Convention on Climate Change, i.e. stabilize greenhouse gas concentration in the atmosphere

LHS Left-hand side

The left-hand side of an equation with respect to the equal sign

NOCT Nominal Operating Cell Temperature

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OECD Organization for Economic Co-operation and Development

Organization to provide a forum for governments and to promote policies to improve the economic and social well-being of the world population

OptMA Lab Optronics and Microtechnology Laboratory

A research laboratory at the electrical engineering department of UFMG under the supervision of Prof. Dr. Davies William de Lima Monteiro

PSPICE Personal Simulation Program with Integrated Circuit Emphasis One of the first release of SPICE for personal computer

RHS Right-hand side

The right-hand side of an equation with respect to the equal sign

SPICE Simulation Program with Integrated Circuit Emphasis

A general purpose electronic simulation program with capabilities of nonlinear dc analysis, nonlinear transient analysis and small signal analysis

SRE Standard Reference Environment

Conditions under which the NOCT is determined:

 Irradiance of 800 W/m2  Ambient temperature of 20°C

 Wind speed of 1 m/s

 Open-rack mounted cell (back side of the cell is open)

 Nil electrical load (open-circuit)

STC Standard Test Conditions

Conditions under which electrical photovoltaic cell parameters are determined:

 irradiance value of 1000 W/m2  Ambient temperature of 25°C

 Light spectrum of AM1.5G

UFMG Universidade Federal de Minas Gerais

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UNITS

Unit

Description

°C Degree Celsius Unit of temperature A Ampere Unit of current

A/°C Ampere per degree Celsius

Unit of a temperature coefficient

C Coulomb

Unit of electrical charge

EJ Exajoule (1018_Joule)

Unit of energy (1J = 2.78*10-7_kWh)

J/K Joule per Kelvin

Unit of heat capacity

K Kelvin Unit of temperature km2 _{Square kilometre} Unit of area kWh Kilowatt-hour Unit of energy (1kWh = 3.6*106_J)

m/s Meter per second

Unit of speed

m2 _{Square meter}

Unit of area

nm Nanometer

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Unit

Description

TWh Terawatt-hour Unit of energy V Volt Unit of voltage

V/°C Volt per degree Celsius

Unit of a temperature coefficient

W/m2 _{Watt per square meter} Unit of irradiance

W/m2_nm1 _{Watt per square meter time nanometer} Unit of irradiance per wavelength

Ω Ohm

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PARAMETERS

Parameter

Unit

Description

AM --- Air mass

Ec --- Nash-Sutcliffe model efficiency coefficient of Castaner´s model towards the fitted model

Ep --- Nash-Sutcliffe model efficiency coefficient of the proposed model towards the fitted model

FF --- Fill factor

FF0 --- ideal fill factor in absence of series resistance and with infinite shunt resistance

G W/m2 Irradiance

I A Output current of a solar module

I0 A Diode saturation current

I01 A Diffusion-diode saturation current

I02 A Recombination-diode saturation current

IC A Output current of a solar cell

IDR A Combined diffusion and recombination current

Im A Current at the maximum power point

Imr A Current at the maximum power point at STC

Iph A Photo-generated current of a solar module

IphC A Photo-generated current of a solar cell

Isc A Short-circuit current

Iscr A Short-circuit current at STC

kB J/K Boltzmann constant (1.38065*10-23)

MADPc % Mean Absolute Deviation Percent of Castaner´s model towards the fitted model

MADPp % Mean Absolute Deviation Percent of the proposed model towards the fitted model

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Parameter

Unit

Description

n1 --- Ideality factor of the diffusion-diode

n2 --- Ideality factor of the recombination-diode

Np --- Number of solar cells in parallel connection

Ns --- Number of solar cells in series connection

Pm W Power at the maximum power point

q C Electric charge (1.60218*10-19₎

Rs Ω Series resistance of a solar module

RsC Ω Series resistance of a solar cell

Rsh Ω Shunt or parallel resistance of a solar module

RshC Ω Shunt or parallel resistance of a solar cell

RMSEc A Root mean square error of Castaner´s model towards the fitted model

RMSEfit A Root mean square error of the fitted model towards the measured data

RMSEp A Root mean square error of the proposed model towards the fitted model

Ta °C Ambient temperature

Tmod °C Temperature of the photovoltaic module/cell

V V Output voltage of a solar module

VC V Output voltage of a solar cell

Vm V Voltage at the maximum power point

Vmr V Voltage at the maximum power point at STC

Voc V Open-circuit voltage

Vocr V Open-circuit voltage at STC

VT V Thermal voltage

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Parameter

Unit

Description

αV V/°C Temperature coefficient of the open-circuit voltage

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CHAPTER 1 RATIONALE

The state electrical energy-distribution company of Minas Gerais, CEMIG, is currently pursuing the goal of installing and operating multiple photovoltaic power plants in Minas Gerais, Brazil´s fourth largest state in regard to area and second largest in regard to population. To achieve that goal CEMIG is in the process of setting up a pilot plant in Sete Lagoas, a city close to the state capital of Belo Horizonte. The aim of the pilot plant is to collect data on the plant’s output and efficiency for later power plants. Furthermore, the plant has a small research area where, in cooperation with the Optronics and Microelectronics Laboratory (OptMA Lab) of the department of electrical engineering at the Federal University of Minas Gerais, the best plant setup and the most effective solar cell type for the present conditions can be determined. In the current time where a growing population means a growing need in energy, it is important that new resources are used to satisfy this need. In addition, increased awareness of pollut io n, especially the harm done by greenhouse gases (1, 2), stimulate the use of renewable and carbon-neutral energy resources. Brazil is already a forerunner in the use of renewable energy sources, especially hydroelectric power. However, this unilateral power production makes Brazil prone to natural disasters, like droughts (3, 4). Thus, Brazil is looking to diversify its power generation to reduce its dependence on the availability of hydropower.

Under the supervision of Professor Dr. Davies William de Lima Monteiro research into the modelling of solar cells and panels is performed. The project described in this report is based on a descriptive problem. It focuses on the accurate simulation of the solar cell output under non-ideal conditions. Especially the temperature dependence of solar cells (5-8) is to be taken into account. Many models are already available to simulate the output of a solar cell based on its physical parameters. However, more often than not those parameters are not available, since manufacturers rather keep their manufacturing process for themselves to strengthen their market position. Hence, it is necessary to develop an accurate model to predict the output of photovoltaic cells based on electrical characteristics measured under certain standard conditions. Physical parameters include the ideality factor, the dark saturation current and the material resistivity. To determine those parameters extensive experime nts and calculations are needed, as well as high-priced equipment. On the other hand, electrical parameters, which include the open-circuit voltage, the short-circuit current and the voltage and current at the maximum power point under certain standard conditions, can be determined with affordable equipment, like a curve tracer.

A model, which can simulate solar cells based on their electrical characteristics, could as well be favourable for manufacturers of photovoltaic cells. When new cells are developed or the production recipes of available solar cells are improved, the manufacturer can simulate the behaviour of the new cell rapidly, after a prototype batch is produced, with easily measurable parameters. That could decrease the risk of developing faulty cells by recognizing production

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errors earlier in the production process. From the modelled I-V curve, the manufacturers can predict the cell´s behaviour under various environmental conditions and identify shortcomings and their possible causes early in the production process.

It is desired to simulate the output of a photovoltaic cell accurately to determine the best suitable cell for power plants in Minas Gerais. The model should only use easily quantifiab le electrical characteristics as inputs, to be able to simulate even little known and litt le-documented solar cells and modules. It should predict the solar cell output with an acceptable accuracy and under varying temperatures and irradiance values.

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CHAPTER 2 SITUATIONAL & THEORETICAL ANALYSIS

This chapter will first analyse the current situation with a short outlook on the future of energy generation. Then the theory behind photovoltaic cells and how they can be modelled is shown. Furthermore are the stakeholders involved in this project described.

2.1 Energy future

The world population grows every year by about 1% (9), which, although declining, will increase the number of humans living on earth to 9.3 billion in the year 2050. Naturally, an increase in the population means an increase in energy needs as well. In 2013 the World Energy Council presented a study in which two different scenarios were characterized and analysed to describe the world and especially its energy needs in 2050 (10). The first scenario, called Jazz, assumes a consumer-focused world where the achievement of energy access, quality of supply and affordability while using the best available sources is a primary goal. Hence, multi- natio na l companies and price-conscious consumers are the driving forces and the main part of the energy will be produced using fossil fuels (i.e. coal, oil and gas). The second scenario is called Symphony. In it, a voter consensus on environmental sustainability and energy security is assumed. Governments and their policies will be the driving forces in this scenario, where the use of fossil fuel for the energy generation will decline and renewable and environmenta l ly friendly technologies will fill the gap.

Energy is classified as primary, secondary and final energy. Primary energy is the energy extracted from its sources while the physical or chemical characteristics are not changed (e.g. crude oil, coal, biomass, solar radiation) (11). On the contrary, there is secondary energy, which is the energy after transformation into electricity, fuel, heat or others. Secondary energy is always less than primary energy due to conversion losses (11). The energy consumed by the consumer is called final energy, which is even less than secondary energy due to transportatio n losses and others. Figure 2-1 describes the earlier mentioned relationship between the population and the primary energy need. The data shown until 2010 is real historic data obtained from (9) and (12) for the population and primary energy, respectively. The data after 2010 are predictions made by (10) in the symphony scenario. The data from this scenario was chosen since the world leaders are already trying to pave the way for a global consensus to support and promote renewable energy sources as well as to stabilize the greenhouse gas concentration in the earth´s atmosphere. One of the first steps in this direction was made with the Kyoto Protocol (13), an international agreement to reduce greenhouse gas emission. It entered into force in 2005, however, only 38 of the participating parties (to date 192 of which only 83 initially signed the protocol) committed to specific reduction targets between 2008 and 2012. In 2009 114 countries agreed on the Copenhagen accord, in it no specific greenhouse gas reduction targets are set, but the signatories recognize the critical impact of climate change and agreed, among others, on the following:

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Figure 2-1 Primary energy supply in relation to the world population

It is apparent, that the primary energy needs rise with a growing population. The historic populati o n data is extracted from (9), the historic data for the primary energy supply is from (12) and the predicte d data is from the Symphony scenario of (10)

“2. We agree that deep cuts in global emissions are required according to science, and as documented by the IPCC Fourth Assessment Report with a view to reduce global emissions so as to hold the increase in global temperature below 2 degrees Celsius, and take action to meet this objective consistent with science and on the basis of equity. We should cooperate in achieving the peaking of global and national emissions as soon as possible, recognizing that the time frame for peaking will be longer in developing countries and bearing in mind that social and economic development and poverty eradication are the first and overriding priorities of developing countries and that a low-emission development strategy is indispensable to sustainable development.”(2)

In 2012 the Doha Amendment to the Kyoto Protocol (14) was adopted in which greenhouse gas reduction targets are set for the period between 2013 and 2020. However, until now only 22 parties accepted the amendment. At the latest climate conference in Lima (15) in December 2014 the initial funding of the Green Climate Fund (GCF) was achieved. The GCF´s target is to significantly contribute to the reduction in global emissions (16), i.e. the emission of greenhouse gases, e.g. carbon dioxide, methane, nitrous oxide and fluorinated gases. The largest part with 26% resulted from energy supply excluding transportation (17), hence mostly electricity generation. Therefore, it is not surprising that one of the three pillars to achieve deep reductions in the carbon dioxide emissions, the most common greenhouse gas (17), is the production of low-carbon electricity by replacing fossil fuel based generation with renewable

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energy sources, nuclear power or fossil fuel based generation with carbon capture and storage (CCS) capabilities (1). This can as well be seen in Figure 2-2 where the predicted electric it y mix in 2050 is shown according to the Symphony scenario. The generation of electricity from oil and coal will decline and renewable energy sources, i.e. solar, hydro and wind energy, will take their places together with coal, gas and biomass based generation with CCS. Of all the renewable energy sources, solar energy is predicted to grow the most, from 34TWh in 2010 to 7741TWh in 2050. That is attributed to the environmental concerns with other renewable energy sources. Hydropower requires usually a large intervention in the rivers ecosystem as well as a storage basin. The noise pollution associated with the generation of energy from wind is high as well as the visual pollution. Both of which are important aspects to consider, due to their sensitivity in the acceptance of local communities. Lastly, geothermal power production possesses the risk of toxic gas release and uses about a third of their produced energy for operations within the plant (18). Additional high initial investments make it an unattractive choice for energy suppliers (19).

Figure 2-2 Predicted electricity generation between 2010 and 2050 by source

The use of fossil fuels without CCS will decrease in the future and renewable and low-carbon energy sources will take their places in the energy mix in 2050. The data is obtained from the Symphony scenario of (10)

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2.1.1 Energy production in Brazil

The energy sector of Brazil is one of the least carbon intensive in the world (1, 20). With only 2.4 metric tons of carbon dioxide produced per person in 2011 (21) it is only second to India in a comparison of all OECD and BRIC countries. In 2013 more than 45% of its primary energy production came from renewable sources, e.g. hydro, wind or biomass, (Figure 2-3) and more than 70% of its electricity supply is from hydroelectric power plants (Figure 2-4). Therefore,

Figure 2-3 Primary energy production of Brazil in 2013

53.6% are produced using non-renewabl e sources, i.e. petroleum, natural gas, coal and nuclear power, and 46.4% are produced with renewable energy sources, i.e. sugar cane products, hydroelectric, firewood and other renewable sources. The data is adopte d from (22).

Figure 2-4 Electricity supply of Brazil in 2013 79.3% of the electricity is supplied by renewabl e sources, i.e. hydroelectric, biomass, wind and the imported electricity, which is mainl y hydroelectric energy. Only a small amount of 20.7% is produced using non-renewable energy sources, i.e. natural gas, oil, coal and nuclear energy. The data is adopted from (23)

Brazil does not have to worry too much on cutting back on its greenhouse gas emissio ns. However, this rather unilateral electricity generation does have its pitfalls as well. Hydroelectric power is vulnerable to droughts, as it happened in 2001 (4) and again nearly in 2013 (3). Power shortages can severely damage the countries industry and scare away future investors. Hence, Brazil has to diversify its electricity generation capacities, to ensure covera ge even in droughts, which might happen more often in the following years, due to the climate change (24). The generation of electricity from solar radiation will become a major player . Firstly, this is especially interesting for Brazil considering its high solar potential as seen in Figure 2-5. The highest level of irradiation is measured in a belt from the northeast to the southwest. Much lower levels occur in the Amazon region, in the north of Brazil, and in the coastal regions in

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Figure 2-5 Annual average of daily inclined solar irradiation in Brazil (25) The irradiation is represented on a plane tilted in an angle equal to the latitude of the point on the map. Yellow and light red colours showing high irradiation, whereas dark red and purple show low irradiation.

the south of Brazil. The low levels in the Amazon region are due to its annual rain season, where clouds reflect much of the sunlight, hence diminishing the annual average solar irradiation levels. In 2011 Brazil could have covered all its electricity needs by covering a 2400km2_{area with an average annual solar irradiation of 1400kWh/m}2_{with solar panels (26).} Secondly, Brazil does not have a 100% electrification rate. Especially small villages in rural areas and the amazon region are not connected to the national power grid. With the use of solar energy systems, in combination with energy storage modules, the electrification of the whole country can be achieved.

2.2 Solar resources

The radiation received on the earth surface form the sun is dependent on many factors, e.g. location on earth, time, weather or season. The path length of the sunlight through earth´s atmosphere is referred to as air mass (AM), due to the fact that the light has to pass thro ugh this mass of air. Upon entering the Earth´s atmosphere sunlight is scattered, absorbed and reflected by the gasses and particles in it. These effects increase when clouds are present. When

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the angle φ between the sun and the point directly overhead is known, the AM can be approximated by (27):

𝐴𝑀 = 1

cos 𝜑 ( 2-1 )

When φ=0° the air mass is AM1G and when φ=46.2° the air mass is AM1.5G, which is the standard spectrum of the sun used in photovoltaics. The spectrum of AM1.5G is shown in Figure 2-6. The spectrum depicts the spectral irradiance for each wavelength. The integral of the spectral irradiance over all wavelengths is the irradiance with its unit W/m2_{. The dips at} around 750, 950, 1150 and 1400 nm are due to light absorption of atmospherical gases, i.e. oxygen, water vapour and carbon dioxide.

Figure 2-6 Spectrum of AM1.5G

2.3 Photovoltaics

Photovoltaic is the method to generate electricity from solar irradiation. Alexandre-Ed mo nd Becquerel first observed the effect in 1839. He discovered that a photocurrent is produced, when silver chloride in an aqueous solution is connected with platinum electrodes. In 1906 photoconductivity was first observed in an organic compound, Anthracene (28). It was later used as photoreceptors in imaging systems. Scientific interest in the 1950s and 60s led to increased research into photoconductivity and related subjects, e.g. photovoltaics. This led to the development of the first inorganic solar cell at Bell Laboratories (29) in 1954. This marked the start for the commercial exploration of solar energy. Today many different solar cell structures exist. The most important ones are silicon, cadmium-telluride, CIGS and

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multijunction solar cells. CIGS are made of copper, an alloy of indium and gallium and selenium, hence the name CIGS, from its chemical formula CuInGaSe2. Multijunction solar cells are produced by stacking single junction cells, like the aforementioned ones on top of each other to achieve a better overall efficiency and a higher voltage output (30).

2.3.1 Operating principle

Many solar cells are made from silicon, a semiconductor material. The cell is a p-n junction in which current is generated through diffusion and drift of holes and electrons generated by absorbed photons. Silicon has 14 electrons of which four are situated on the outer shell of the Bohr-model (Figure 2-7). Those four valence electrons can be shared with other silicon atoms. Figure 2-8 shows schematically the structure of a simple silicon solar cell. It consists of 2 layers that exhibit different electrical properties, which are determined through doping with foreign atoms. The p-layer is much thicker than the n-layer and is produced through the replacement of some silicon atoms with a trivalent element, e.g. elements of the third group of the periodic table. Those elements only have three valence electrons on the outer shell, thus introducing a hole, which can be filled by neighbouring electrons leaving holes at their original positions. In the n-layer some silicon atoms are substituted with atoms of pentavalent elements at high

Figure 2-7 Bohr model of silicon (31) Silicon has 14 electrons, which are organized on three shells. 2 electrons on the first shell, eight on the second and four on the third and outermost shell.

Figure 2-8 Schematic drawing of a silicon solar cell (32) Basic components are the p-layer, doped with trivale nt elements, the n-layer, doped with pentavalent elements and a metal grid on the front and a complete metaliz e d back for charge collection

temperatures. Such elements are phosphorus, arsenic and antimony. They have five valence electrons on the outer shell, hence introducing a surplus electron which can be ionized easily (33). The n-layer is called the donor layer and the p-layer the acceptor layer. The back of the cell, i.e. the acceptor layer side, is usually completely metalized for charge collection. On the contrary, on the front there is only a metal grid applied. The grid is sparse enough to allow light to pass through to the solar cell material and to collect charges.

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The area where both layers intersect is called the p-n junction. Along it, free electrons from the donor layer will diffuse into the p-layer to combine with the holes. At the same time excess holes from the acceptor layer diffuse into the n-type material. This process leads to a negative charge build-up on the p-layer side of the junction and a positive charge build-up on the n-layer side of the junction. Therefore, an electric field is generated in the area around the p-n-junction, the so-called space-charge region or depletion region. This field prevents electrons and holes from farther away to diffuse in the opposing layer. Within the depletion region electrons and holes are still moving around, generating small currents which counteract each other. Thus an equilibrium is reached that results in a null net current. Figure 2-9 shows the effect of sunlight on the solar cell. When photons, with enough energy to split the bond between an electron and a silicon atom, hits the solar cell an electron-hole pair is generated. If that pair is generated in the p-layer of the cell the electron will meander around freely to recombine with a hole. However, due to the design of the cell it is likely that the free electron will encounter the junction before it can recombine with a hole. Within the field of the junction the electron is accelerated across the barrier into the donor layer. The minor amount of holes in the donor layer significantly reduces the chance of recombination with a hole. Furthermore is it not

Figure 2-9 Schematic of the operating principle of a silicon solar cell (34)

Electrons formed in the p-layer and holes formed in the n-layer move across the p-n junction, which creates a light induced charge imbalance. The electrons then move through the external circuit form the n-layer to the p-layer generating a current.

possible for the electron to cross back into the p-layer, due to the electric field generated along the junction. If the electron-hole pair is created in the n-layer of the solar cell the free electron is rejected by the barrier, but the hole is filled by valence electrons from the p-layer, thus the hole moves over to the acceptor layer of the cell. When the n-layer and p-layer of the solar cell are now connected through an external circuit a current will flow. The electrons from the donor layer will move through the circuit into the acceptor layer, to reduce the light induced charge imbalance (35).

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2.3.2 Photovoltaic characteristics

There are many parameters involved in the characterization of a solar cell however, the most important one are the short-circuit current (Isc), open-circuit voltage (Voc) and the maximum power point (Pm) which is described by its current (Im) and voltage (Vm). All of those parameters are shown in Figure 2-10. Isc is the maximum current the photovoltaic cell can produce, but the voltage is 0, hence the power is 0. Voc is the maximum voltage the cell can produce, however the current is 0 at this point. Pm is the point where the cell delivers the maximum power. During operation, the system should operate at the voltage of the maximum power point, to ensure the highest possible efficiency for the solar cell.

Figure 2-10 Typical I-V curve of a photovol taic cell

With the most important parameters (Isc, Voc, Pm (Vm, Im)) marked on the graph

These parameters are often given by the manufacturer under standard test conditions (STC). If that is not the case they can easily be determined using the proper equipment, e.g. a source meter. To quantify the quality of a photovoltaic cell another parameter is used, the fill factor (FF). It is defined as: 𝐹𝐹 = 𝑃𝑚 𝑉𝑜𝑐 ∗ 𝐼𝑠𝑐 = 𝑉𝑚∗ 𝐼𝑚 𝑉𝑜𝑐∗ 𝐼𝑠𝑐 ( 2-2 ) It basically describes how well the rectangle defined by Vm and Im fills the rectangle defined by the open-circuit voltage and the short-circuit current. The closer the value is to unity, i.e. 1, the better is the performance of the photovoltaic cell.

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2.3.2.1 Test conditions

To compare different photovoltaic cells, standard test conditions (STC) are specified. Parameters, like the open-circuit voltage and short-circuit current, measured under those conditions are often provided by the manufacturers or research institutions. The measureme nt conditions are (36):

 irradiance value of 1000 W/m2

 Cell/Module temperature of 25°C

 Light spectrum of AM1.5G

Another set of specified test conditions is used to determine the nominal operating cell temperature (NOCT). NOCT is the operating temperature of the photovoltaic cell at specified conditions, i.e. the standard reference environment (SRE) (37):

 Irradiance of 800 W/m2

 Ambient temperature of 20°C

 Wind speed of 1 m/s

 Open-rack mounted cell (back side of the cell is open)

 Nil electrical load (open-circuit)

With the NOCT the actual cell operating temperature for different ambient temperatures and irradiation values can be calculated with the following expression:

𝑇_𝑚𝑜𝑑 = 𝑇_𝑎+𝑁𝑂𝐶𝑇 − 20

800 ∗ 𝐺 ( 2-3 )

where Tmod and Ta are the cell operating temperature and ambient temperature respectively in °C, NOCT is the nominal operating temperature in °C and G is the solar irradiation in W/m2_. The 20 and 800 are the ambient temperature and Irradiance in SRE, respectively.

2.3.3 Factors influencing solar cell output

The ideal I-V curve of solar cells, as depicted in Figure 2-10, is only very rarely found under real operating conditions. Many factors influence the output of a photovoltaic cell. Those factors, among others, are the ambient temperature, the irradiance and the series resistance. The various effects can be seen in Figure 2-11.

2.3.3.1 Irradiance effects

Part (a) of Figure 2-11 shows the effect of changing irradiance on the I-V curve of a solar cell. As seen in chapter 2.3.2.1 above, the irradiance influences the operating temperature of the cell. However, this effect is not represented in Figure 2-11 (a), since the irradiance more importantly influences the amount of current generated. When less light arrives at the solar cell, then logically less electron-hole pairs are generated, where the electrons and holes are moved across the p-n junction, thus resulting in a lower charge imbalance and a lower current. From Figure 2-11 (a) it is apparent that the short-circuit current is directly proportional to the irradiance. In addition to the effects on Isc, the irradiance affects the open-circuit voltage as well. However, Voc is only logarithmically proportional to the irradiance. Summarizing, the

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irradiance affects the short-circuit current greatly, but only small effects are observed on the open-circuit voltage.

Figure 2-11 Factors influencing photovoltaic cell output

(a) Effects of irradiance on the I-V curve, adopte d from (38)

(b) Effects of temperature on the I-V curve, adopted from (39)

(c) Effects of series resistance on the I-V curve, adopted from (40)

2.3.3.2 Temperature effects

A change in ambient temperature leads directly to a change in the operating temperature according to the NOCT equation, i.e. equation 2-3. With an increase in temperature the bandgap energy of the semiconductor decreases marginally, thus electron-hole pairs can be created with less photon energy. This results in an slight increase in the short-circuit current (27). Opposed to that, the open-circuit voltage is decreased significantly with increasing temperature. The decrease in bandgap energy results in a significant increase in the intrinsic carrier

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concentration, since electrons can break away from their atoms more easily. This increase does in turn increases the dark saturation current which leads to the decrease in Voc (8, 27). Figure 2-11 (b) shows this effect. The open-circuit voltage is decreasing significantly with increasing temperature, whereas the short-circuit current increases only slightly.

2.3.3.3 Series resistance effects

In solid states physics, specifically semiconductor physics, it is widely known how semiconductor diodes react on changes in temperature. A solar cell, made from semiconduc tor material, is effectively a p-n junction diode. Those diodes are researched extensively and four distinctive regions have been identified in the forward bias characteristics. When plotting the voltage-current characteristic on a semi-logarithmic scale, i.e. log(I) vs. V, the four regions can be identified easily (41). Figure 2-12 shows such a typical forward bias characteristic of a p-n junction diode. The dotted lines represent the slopes of the different parts of the curve. The blue part of curve is caused by the recombination of electrons and holes within the

Figure 2-12 Typical forward bias characteristic of a p-n junction diode Plotted on a semi-logarithmic scale with its four distinctive regions visible.

depletion region. The so created current does not benefit the diode, it therefore dampens the ideal characteristics in the low forward bias region where it dominates. The orange part of the curve resembles the ideal region of the diode. In it the diffusion current, the current generated when electrons move across the junction into the n-layer and holes diffuse into the p-layer, dominates. The deviation from the ideal curve in the grey part of Figure 2-12 is caused by

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level injection. It has a slope much more similar to the first region. The last region, the yellow part of the curve, is the deterioration of the ideal curve due to series resistance of the diode. This series resistance is a combination of the resistivity of the semiconductor, the contact resistance between the semiconductor and the metal contacts and the resistance of the wiring. However, in solar cells the last two regions are rarely exhibited. The open-circuit voltage usually occurs in the higher areas of the ideal region, i.e. the diffusion dominated region. Hence the series resistance as described above does not influence the solar cell output. The series resistance talked about in this report is a deterioration of the I-V characteristics in the ideal region, of the solar cell. The effect of dampening the curve as seen in Figure 2-11 (c) is described by an imaginary series resistance.

This series resistance is decreasing with increasing temperature and increasing irradiance. That can easily be seen when considering the simple diode equation:

I = 𝐼₀𝑒

𝑞(𝑉+𝐼𝑅_𝑠)

𝑛𝑘_𝐵𝑇 ( 2-4 )

where I is the current flowing through the diode, I0 is the dark saturation current, q is the electric charge of electrons, kB is the Boltzmann constant, n is the ideality factor of the diode, T is the absolute temperature in kelvin, Rs is the series resistance and V is the applied voltage across the diode terminals. If we rearranged equation 2-4 to:

𝑙𝑛 [𝐼 𝐼₀] =

𝑞(𝑉 + 𝐼𝑅_𝑠)

𝑛𝑘_𝐵𝑇 ( 2-5 )

it is visible, that the aforementioned effect of the temperature on the dark saturation current together with the decrease of 𝑞

𝑘_𝐵𝑇 lead to the described decrease in the series resistance. An increase in irradiance does cause an increase in I, which as well leads to a decrease in Rs. This is due to the dominance of the I on the RHS of equation 2-5 over the I on the LHS.

Figure 2-11 (c) shows that the short-circuit current is only effected by the series resistance, when it gets significantly large. Since manufacturers try to keep Rs as low as possible, that should not be the case for commercially available photovoltaic cells. Hence, the series resistance affects mostly the maximum power point and therefore the fill factor. An increase in Rs will lead to a decrease in the fill factor and vice versa; a decrease in the series resistance will lead to an increase in the fill factor.

2.4 PSPICE

SPICE stands for Simulation Program with Integrated Circuit Emphasis, which was first described in 1973 (42). It was developed by Laurence Nagel and Donald Pederson as a general purpose electronic simulation program based on the CANCER program (computer analysis of nonlinear circuits, excluding radiation). SPICE has the capabilities of nonlinear dc analysis, nonlinear transient analysis and small signal analysis. All analysis are based on matrix calculations of circuits nodes and loops containing mathematical models of electrical and electronic components (43). PSPICE, standing for personal SPICE was one of the first release

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of SPICE for personal computer. The program analyses a circuit described in a text file or as a schematic. First a netlist is generated, on which the required analysis is run and the results are stored in an output file. These results are then displayed graphically or in a text editor.

2.4.1 OrCAD Capture

OrCAD Capture is one of the most widely used schematic design solutions according to its developers at Cadence Design Systems (44). It combines three main applications: Capture, in which a schematic of the electric circuit is drawn, PSPICE, which can simulate the circuits and analyse its behaviour and a PCB Editor, for the design of printed circuit boards. A free version of OrCAD is available for students and interested engineers. However, it has limitat io ns regarding the number of nets and parts per design and the number of pins per created part. Designs which exceed those limits can be create and viewed, but they cannot be saved.

2.4.2 PSPICE A/D

Figure 2-13 PSPICE A/D interface

PSPICE A/D is a SPICE-based simulator, which is able to simulate both analog and digita l designs. It is fully integrated with OrCAD Capture, thus it easily simulates schematic circuits and performs various analysis on it, e.g. temperature analysis, DC or AC analysis or a Monte Carlo analysis. Once the circuit is simulated PSPICE A/D is able to evaluate many measurements on the active trace. Figure 2-13 shows the PSPICE A/D interface where an I-V curve is plotted and various measurements are evaluated, i.e. the open-circuit voltage, the short-circuit current and the maximum of the P-V curve.

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2.4.3 PSPICE devices

PSPICE can model many common analog devices, e.g. capacitors, inductors, resistors and diodes. For resistor models (Figure 2-14(b)) at least the value of the resistance in Ohm has to be specified. Additionally, linear, quadratic or exponential temperature coefficients can be specified, to improve the model. The model for diodes (Figure 2-14(a)) is more complex than the resistor model. Parameters which can be defined by the user include saturation current, temperature coefficients, emission coefficient and parasitic resistance. All the model parameters have already set default values as specified in (45). Furthermore, PSPICE is able to simulate voltage-controlled voltage sources (Figure 2-14(c)) and voltage controlled current sources (Figure 2-14(d)), which are called e- and g-devices, respectively. These devices set the output voltage or current depending on the input and a specified gain. The gain can be linear or a more complex equation.

Figure 2-14 PSIPCE components in OrCAD Capture (46) (a) Diode with the model specified (Dbreak)

(b) Resistor with its resistance value in Ohm (c) Voltage-controlled voltage source (e-device) (d) Voltage-controlled current source (g-device)

In PSPICE a specific library for analog behavioural modelling (ABM) is available as well. It reflects the structure of e- and g-devices where the differential input of some devices is set to ground (47).

2.5 Solar cell models

To predict the output of photovoltaic cells and to determine possible improvement factors it is important to simulate them. Multiple models have been developed for different purposes. A commonly used model is the single-diode model, which is used in several publications (48-55). As the name suggests it makes use of one diode in parallel with the current source. Another frequently used model, proposed by (56-61), among others, makes use of a second diode in parallel to the current source and is therefore called two-diode model. Although these two models are used by many authors other model have been developed, like the three-diode model proposed by (62). In the following the one- and two-diode model are presented in more detail.

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2.5.1 Single-diode model

As mentioned earlier, this model represents a photovoltaic cell using a current source with a parallel diode (Figure 2-15). The current source simulates the photo generated current IphC and

Figure 2-15 One-diode solar cell model

D1 simulates the diffusion current which counteracts the photo generated current IphC. RsC and RshC represent series and shunt resistive losses, respectively.

the diode D1 the diffusion current which counteracts IphC. The series resistance RsC simula tes the resistance encountered when the generated current travels through the semiconduc tor material, added by eventual contact resistance. The parallel or shunt resistance RshC simula tes a conductance in the depletion region due to atom vibrations as well as production impurit ies. The current flowing through this resistance is called the shunt current. It is the current that finds a way around the p-n junction, thus not generating any power for the solar cell (63). Generally, RsC is very small, whereas RshC is very large. Some authors ignore one or both variables to simplify their models.

The current output in this model is described as follows: 𝐼_𝐶 = 𝐼_𝑝ℎ𝐶 − 𝐼₀(𝑒

𝑉_𝐶+𝐼_𝐶𝑅_𝑠𝐶

𝑛𝑉_𝑇 _{− 1) − (}𝑉𝐶 + 𝐼𝐶𝑅𝑠𝐶

𝑅_𝑠ℎ𝐶 ) ( 2-6 )

where IphC is the photo generated current, I0 and n are the saturation current and ideality factor of diode D1 respectively, RsC is the series resistance and RshC is the shunt resistance. The C in the subscript indicates that those parameters are parameters of photovoltaic cells. When the model is to be used for a photovoltaic module a conversion of this formula according to Appendix A.1 has to be performed. VT is the thermal voltage, which is calculated using Boltzmann´s constant kB=1.38065*10-23_{J/K, the absolute temperature T, in Kelvin, and the} electric charge of electrons q=1.60218*10-19_C.

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19 𝑉_𝑇 =𝑘𝐵𝑇

𝑞 ( 2-7 )

2.5.2 Two-diode model

The two-diode model adds another diode to the aforementioned model. This second diode simulates the recombination effects. They can occur at impurities in the crystal structure or at the surface of the material. When electrons recombine before they are being collected the current output of the solar cell suffers. Hence the recombination current counteracts the photo generated current, just as the diffusion current simulated by D1. Figure 2-16 shows a general two-diode model. Some authors choose to neglect some parameters or combine others, to simplify their models and further calculations.

Similar to equation 2-6 for the single-diode model, the current output for the two-diode model is calculated. The two diodes are represented by the saturation currents I01 and I02 for diode D1 and D2 respectively. Both usually have different ideality factors n1 and n2 as well. Most often they are considered to be n1=1 and n2=2. In the equation the variables are defined as for the single-diode model 𝐼_𝐶 = 𝐼_𝑝ℎ𝐶 − 𝐼₀₁ (𝑒 𝑉_𝐶+𝐼_𝐶𝑅_𝑠𝐶 𝑛₁𝑉_𝑇 _{− 1) − 𝐼} 02(𝑒 𝑉_𝐶+𝐼_𝐶𝑅_𝑠𝐶 𝑛₂𝑉_𝑇 _{− 1) − (}𝑉𝐶 + 𝐼𝐶𝑅𝑠𝐶 𝑅_𝑠ℎ𝐶 ) ( 2-8 ) Figure 2-16 Two-diode solar cell model

D1 and D2 simulating the diffusion current and recombination current respectively, whic h counter act the generated photocurrent IphC, RsC represents the series resistive losses and RshC the shunt resistive losses.

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2.6 Stakeholders

This project is initiated by CEMIG, the state electrical energy-distribution company of Minas Gerais, together with UFMG, Federal University of Minas Gerais. CEMIG is planning to develop multiple photovoltaic power plants in the Brazilian state of Minas Gerais in order to supply cheap and reliable energy to the population and the industry. The first of these plants is installed in Sete Lagoas, close to the states capital. CEMIG is interested in the modelling of photovoltaic cells and later systems to estimate the output of such a power plant. The research is carried out at the Optronics and Microtechnology Laboratory (OptMA Lab) of the department of electrical engineering at UFMG. The head of this lab, Dr. Davies William, is my supervisor for the here presented research. UFMG wants to position itself as the top photovoltaic research university in Brazil. Another stakeholder is Hanze University of Applied Sciences Groningen, although a secondary one. Represented by Mr. Ronald van Elburg and Mr. Bryan Williams as first and second graduation supervisor respectively. They will evaluate the research based on the here presented report and the final presentation.

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CHAPTER 3 CONCEPTUAL MODEL

The general two-diode solar cell model requires that physical parameters, i.e. diffusion current, recombination current and shunt and series resistance, are known. But more often than not this is not the case. If solar cells have to be evaluated for new applications, the manufactur ers provide relevant electrical data measured under STC or in the SRE. To obtain physical parameters from material databases is not always practical, since manufacturers might use materials, which are not yet listed in those databases, or they improved already known materials, thus altering their physical parameters. Therefore, it is of great value to model photovoltaic cells with only the available electrical parameters. The model described in detail in this chapter is able of doing so.

3.1 General concept

Figure 3-1 Flowchart of the general concept

The concept will largely focus on the accurate modelling of the solar cell, so that a good estimation on the power generation under changing conditions can be given. To be able to

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model the photovoltaic cell in PSPICE certain parameters defining the cell have to be determined. Those electrical parameters are:

 short-circuit current (Iscr)

 open-circuit voltage (Vocr)

 current at the maximum power-point (Imr)

 voltage at the maximum power-point (Vmr)

 temperature coefficient of the short-circuit current (αI)

 temperature coefficient of the open-circuit voltage (αV)

 NOCT

where the first four are determined under standard test conditions, hence the subscript r for reference. If they are not provided from the manufacturer of the solar cell or if the solar cell is a new development, then the parameters have to be measured using suitable equipment. After determining the reference currents and voltages under STC the temperature coefficients are calculated. To do so the short-circuit current and open-circuit voltage are measured under conditions similar to STC where only the temperature is changed. From the difference between Iscr and Vocr and the other set of short-circuit current and open-circuit voltage, change in the current and voltage per °C, thus the temperature coefficients are calculated. The last parameter, the NOCT, is determined within the standard reference environment. The parameters can then be inserted into the PSPICE model to predict the I-V curves with its maximum power-point under conditions different from the reference conditions. Furthermore, it is possible to load the temperature and irradiance data from one day into the model, which will then simulate the expected output during the whole day.

3.2 Proposed solar cell model

The proposed model is based on the model developed by Castaner (64), however its governing equations are based on the two-diode model instead of the single-diode model. Furthermore, the newly proposed model does incorporate the temperature dependence of the series resistance, which shall result in a more accurate prediction of the fill factor. The principal of purely using electrical parameters as inputs for the model is kept. That enables the quick evaluation of newly developed solar cells or modules for which physical parameters, e.g. ideality factor or diode saturation current, necessary for the two-diode model, are not yet available. The electrical parameters can easily be obtained from the manufacturer´s datasheet, experiments or published research articles. Hence, the proposed model can be valuable to the evaluation of newly designed photovoltaic cells and modules, as well as for cells/modules to which no extensive documentation is available, due to reasons of secrecy or negation.

Figure 3-2 shows a schematic of the proposed model. The actual model (red frame) consists of three voltage controlled current sources, i.e. Girrad, Gidiode and Gs, and a resistor Rsh in parallel to Girrad and Gidiode. This resistor represents the shunt resistance, which is assumed very large, i.e. 100GΩ. Girrad represents the photo-generated current Iph. This current is counter acted by the currents through the recombination and diffusion diode. These currents are combined in the voltage controlled current source Gidiode. The series resistance is simulated by the last g-device (Gs), where the controlling and output nodes are the same. With

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23 Figure 3-2 Schematic of the proposed solar cell model

The schematic is adapte d from (62), it depicts the actual model (red frame) and voltage-control l e d sources which calculate important cell parameters (blue frame) used in the model

it a conductance is simulated (65), which is the inverse of the resistance. Hence the voltage between the two controlling nodes divided by the resistance will generate the appropriate conductance to represent the desired series resistance. Node 302 is the input node for the irradiance, which is then used in many of the e- and g-devices to calculate the cell parameters and its overall output. The second input node, 303, is for the ambient temperature. If it is desired to simulate the output of a solar cell or module over the whole day, or week for that matter, than the irradiance and ambient temperature at previously specified times of the day can be input as a time series. The model then calculates the output of the cell or module at each time and a curve of the output vs the time is the result. If, however, the temperature effects on the cell are to be evaluated it is sufficient to use the PSPICE setting for the temperature. A series of temperatures can be set as well in these settings, but PSPICE will start for every temperature a new analysis. Hence, it is not sufficient if an output profile of the whole day is needed. At node 304 the output of the solar cell can be read.

The devices within the blue frame in Figure 3-2 calculate important photovoltaic cell parameters, which are used in the model and can be read out at the specified nodes. The devices Isc and Im calculate the short-circuit current Isc at node 305 and the current at the maximum power point Im at node 308, respectively. The resistors risc and rim are only to avoid floating nodes in the simulation, however their very small resistance values will not affect the simulation. At nodes 306 and 309 the open-circuit voltage and voltage at the maximum power point Vm are calculated by the e-devices Voc and Vm respectively. The e-device Tmod will calculate the cell operating temperature according to equation 2-3. Thus the voltage output at node 307 represents a temperature in °C.

Proposed solar cell model

Electrical characterization of photovoltaic cells to predict cell performance